`@` `\text {Ans}`
`\downarrow`
\((3x^6y^7z^6 + 2x^5y^3z^7 - 6x^5y^3z^8) \div 42x^3y^3z^6\)
`= 3x^6y^7z^6 \div 42 x^3 y^3 z^6 + 2x^5 y^3 z^7 \div 42x^3 y^3 z^6 - 6x^5 y^3 z^8 \div 42x^3 y^3 z^6`
`= 1/14 x^3 y^4 + 1/21 x^2 z - 1/7 x^2 z^2`
\(\left(3x^6y^7z^6+2x^5y^3z^7-6x^5y^3z^8\right):42x^3y^3z^6\)
\(=\dfrac{3x^6y^7z^6}{42x^3y^3z^6}+\dfrac{2x^5y^3z^7}{42x^3y^3z^6}-\dfrac{6x^5y^3z^8}{42x^3y^3z^6}\)
\(=\dfrac{x^3y^4}{14}+\dfrac{x^2z}{21}+\dfrac{x^2z^2}{7}\)